Tel Aviv University
This week's Horowitz seminar will feature TWO speakers.
NOTE THE SPECIAL START TIME!!!
Monday, December 12, 2011
We will start at 14:10 sharp with Alexandre Stauffer
from Microsoft Research who will speak for the first hour. Then, after a short
break, we will continue with Tom Ellis from Tel Aviv University
speaking for the second hour. We will end at 16:00.
Meeting place is room 309 as usual.
Stauffer title: Space-time percolation and detection by mobile nodes.
Consider a Poisson point process of intensity lambda in R^d. We
denote the points as nodes and let each node move as an independent
Brownian motion. Consider a target particle that is initially placed
at the origin at time 0 and can move according to any continuous
function. We say that the target is detected at time t if there
exists at least one node within distance 1 of the target at time t.
We show that if lambda is sufficiently large, the target will
eventually be detected even if its motion can depend on the past,
present and future positions of the nodes. In the proof we use
coupling and multi-scale analysis to model this event as a fractal
percolation process and show that a good event percolates in space
Ellis title: The Brownian web is a two dimensional black noise.
The Brownian web is a stochastic process constructed from Brownian
motions, and was one of the first known examples of a "black noise"
in the sense of Tsirelson. I will discuss what it means to be a black
noise, and demonstrate how the Brownian web is in fact a
two-dimensional black noise. It is only the second known example of a
two-dimensional black noise after Schramm and Smirnov's result on the
scaling limit of critical planar percolation.
Joint work with Ohad Feldheim.
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel <email@example.com>
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